Subject: Geometry
Subject: Geometry
Grade Level: High School
Unit Title: Plane Geometry |Timeframe Needed for Completion: 23 days
Grading Period: 2nd 9 weeks | |
|Big Idea/Theme: Solving problems involving plane figures |
| |
|Understandings: |
|Parallelograms, Trapezoids and kites, Area of plane figures , Relationships between similarity ratio, ratio of perimeters, and ratio of areas |
|Circles, arcs and sectors |
|Essential Questions: |Curriculum Goals/Objectives |
|How do the properties of parallelograms and parallel lines interrelate? |G.CO.11 Prove theorems about parallelograms. Theorems include: |
|How do you find the area of a plane figure? |opposite sides are congruent, opposite angles are |
|How do the arc length formula and the area of a sector formula work? |congruent, the diagonals of a parallelogram bisect each |
|What is geometric probability? |other, and conversely, rectangles are parallelograms with |
| |congruent diagonals. |
| |G.SRT.5 Use congruence and similarity criteria for triangles to |
| |solve problems and to prove relationships in geometric |
| |figures. |
| |G.GPE.4 Use coordinates to prove simple geometric theorems |
| |algebraically. For example, prove or disprove that a |
| |figure defined by four given points in the coordinate plane |
| |is a rectangle; prove or disprove that the point (1, ) |
| |lies on the circle centered a the origin and containing the |
| |point (0, 2). |
| |G.CO.1 Know precise definitions of angle, circle, perpendicular |
| |line, parallel line, and line segment, based on the |
| |undefined notions of point, line, distance along a line, and |
| |distance around a circular arc. |
| |G.CO.13 Construct an equilateral triangle, a square, and a regular |
| |hexagon inscribed in a circle. |
| |G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a |
| |triangle by drawing an auxiliary line from a vertex |
| |perpendicular to the opposite side. |
| |G.C.1 Prove that all circles are similar. |
| |G.C.5 Derive using similarity the fact that the length of the arc |
| |intercepted by an angle is proportional to the radius, and |
| |define the radian measure of the angle as the constant of |
| |proportionality; derive the formula for the area of a sector |
| |G.GPE.7 Use coordinates to compute perimeters of polygons and |
| |areas of triangles and rectangles, e.g., using the distance |
| |formula.* |
| |G.MG.1 Use geometric shapes, their measures, and their properties |
| |to describe objects (e.g., modeling a tree trunk or a human |
| |torso as a cylinder)* |
| |G.C.2 Identify and describe relationships among inscribed |
| |angels, radii, and chords. Include the relationship |
| |between central, inscribed, and circumscribed angles; |
| |inscribed angles on a diameter are right angles; the |
| |radius of a circle is perpendicular to the tangent where |
| |the radius intersects the circle. |
| |G.C.3 Construct the inscribed and circumscribed circles of a |
| |triangle, and prove properties of angles for a quadrilateral |
| |inscribed in a circle. |
| |G.C.4 (+) Construct a tangent line from a point outside a given |
| |circle to the circle |
| |G.GPE.1 Derive the equation of a circle of a given center and radius |
| |using the Pythagorean Theorem; complete the square to |
| |find the center and radius of a circle given by an equation |
| |G.GPE.2 Derive the equation of a parabola given a focus and |
| |directrix. |
| |G.GMD.4 Identify the shapes of two-dimensional cross-sections of |
| |three- dimensional objects, and identify three-dimensional |
| |objects generated by rotations of two-dimensional objects |
| | |
|Essential Skills/Vocabulary: |Assessment Tasks: |
|Consecutive angles |Use the properties of parallelograms and quadrilaterals to find angles and sides of polygons. |
|Isosceles trapezoid |Find the area of plane figures |
|Special parallelograms |Find the circumference of a circle |
|Apothem of a regular polygon |Find the arc length of a portion of the circle |
|Central Angle |Find the area of a circle |
|Inscribed angle |Find the area of a sector of a circle |
|Intercepted arc | |
|Tangent | |
|Point of tangency | |
|Secant | |
|Materials Suggestions: |
|Prentice Hall Geometry |
|McDougal Littel Geometry |
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